Everyone's different, but I can volunteer my own personal experience.
At the moment I'm about three and a half weeks in to a buprenorphine detox and I'm still just about in acutes. I'm using a lot of sleep meds every night to sleep, which I'm going to have to tail off soon.
The medical communities generalised opinion on things is that it takes five half lives for a drug to be eliminated from your system, so that would be 200 hours on average for buprenorphine. However, it's not as simple as all that and your brains natural systems that release neurotransmitters that bind to the opiate receptors can still be firing back up when you have some of the drug left in your brain.
If you are in withdrawal, that's good news! It means your body is moving towards operating naturally again. Maybe you could use some non-recreational sleep aids to get you to sleep? Much better than using more bupe and setting the process back.
I'll be completely honest here and set out what I'm using at the moment for sleep. I'm not for one second you recommend using all this, but this is just how I'm getting through my detox. I was using....
200mg quitiapine
15mg zopiclone
10mg zolpidem
30mg promethazine
4mg melatonin
I've now run out of the z drugs and am using....
200mg quitiapine
60mg promethazine
4mg melatonin
3-5mg etizolam (I know that this can be recreational, but I'm on a diazepam script but it has zero recreational effect for me and simply helps out with sleep)
I wouldn't for a second recommend using all that. I would starrt off by maybe trying just the melatonin and seeing if that works, if it doesn't maybe add in some diphenhydramine. I'm in the process of reducing my nightly meds, as soon as I'm out of the acutes I'll cut down to maybe just the melatonin and promethazine, then just the melatonin, then nothing.
I have no idea if that's been of any help but that's what I personally have to offer on the matter.